Scientists at Stanford University in California have been developing gloves, based on the ingenious methods of geckos, which will enable humans to be able to scale vertical objects.
They've created adhesive hand pads which incorporate a silicone material called polydimethylsiloxane, which is layered as microscopic wedges. They then use van der Waals force, similarly to geckos, to keep the user attached. The full scientific explanation can be found here, which the video below shows a 70kg climber ascending a 3.7 metre vertical glass surface.
Currently their invention only works on smooth surfaces such as glass and plastic, so we're a way off full spider, or rather gecko-man status yet, but give it another 20 years and we'll be able to jump off our hoverboards and climb up the nearest building with ease.